Fourier transforms of polytopes and their role in Number Theory and Combinatorics

Sinai Robins (University of Sao Paulo, Sao Paulo, Brasil and Brown University, Providence, USA)
December 21, 2017 — 11:15 — "Salle du conseil du L2S"

Abstract

Abstract: We introduce the topic of the Fourier transform of a Euclidean polytope, first by examples and then by more general formulations. Then we point out how we can use this transform (and the frequency space) to analyze the following problems: 1. Compute lattice point enumeration formulas for polytopes 2. Relate the transforms of polytopes to tilings of Euclidean space by translations of a polytope We will give a flavor of how such applications arise, and we point to some conjectures and applications.